anonymous
  • anonymous
Find the sum of the geometric series. 5 Σ 2(-4)k k=1
Mathematics
jamiebookeater
  • jamiebookeater
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dumbcow
  • dumbcow
is that (-4)^k or (-4)*k
dumbcow
  • dumbcow
since its geometric, ill assume k is the exponent 2 is a constant so it can be pulled out of sum formula for sum of geometric sequence is \[s _{n}=\frac{a _{1}(1-r ^{n})}{1-r}\] r = -4, n =5, a=-4 s = -4(1-(-4)^5)/(1-(-4)) s = -4(1+1024)/5 s = -820
dumbcow
  • dumbcow
oops then multiply by 2 s = -820*2 s=-1640

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anonymous
  • anonymous
but wait a min, since it's a geometric series, you'lk have to take the absolute value of r , |r| = |-4| = 4 >1, in this case, since R > 1 then the following series is said to diverge, right? .-.

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